Conventionally, an outer cable for guiding a control wire of a bicycle has at one end an end cap attached thereto and is supported therethrough to an outer cable holder provided at an operating lever, a brake or a derailleur. The end cap used for the outer cable, as disclosed in FIG.4 of Japanese Utility Model Publication Gazette No. Sho 55-23,211, is tubular and has at its bottom an insertion bore for the control wire. Since an inner diameter of the insertion bore is larger than an outer diameter of the control wire, a gap is created between the insertion bore and the control wire. Accordingly, while the bicycle is running, mud or the like spattered from the bicycle wheel and attached to the surface of the control wire exposed from the outer cable may enter into the outer cable through the gap when the control wire moves relative to the outer cable, with the result that resistance against movement of the control wire relative to the outer cable is increased. Hence, a problem is created in that the operability of the control wire becomes worse and the outer cable and control wire are damaged, become rusted or deteriorated in durability.